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Find the first three non-zero terms of a power series for ${ e }^{ { x }^{ 2 } }$ centered at $0$ and use them to estimate the given integral $\int _{ 0 }^{ 1 }{ { e }^{ { x }^{ 2 } } } dx$.

A

$1+e+\frac { 1 }{ 2 } { e }^{ 2 }$

B

$1+1+\frac { 1 }{ 2 } $

C

$1+\frac{1}{2}+\frac{1}{6}$

D

$1+\frac { 1 }{ 3 } +\frac { 1 }{ 10 } $

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